Download Dynamics of Flexible Multibody Systems: Rigid Finite Element by Edmund Wittbrodt PDF

By Edmund Wittbrodt

A new technique is gifted for modelling multi-body structures, which constitutes a considerable enhancement of the inflexible Finite aspect technique. the recent method relies on homogeneous ameliorations and joint coordinates, and it yields the virtue that equations of movement are immediately generated for platforms such as exchange inflexible and versatile hyperlinks. except its uncomplicated actual interpretation and simple computing device implementation, the strategy is usually worthwhile for academic reasons because it impressively illustrates the effect of mechanical positive factors at the mathematical version. This novel modelling method is then utilized to platforms resembling offshore-cranes and telescopic rapiers.

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78a) P=  P3  ,  0  M1  M2   M=  M3  . 78b) In Fig. 13 force P acts on the body at point N in the local coordinate system { } . 43) any vector from the system { } can be defined in the system { } by using transformation matrix B, which depends on the { } Xˆ 3 { }9 N Xˆ 93 P9 r9 Xˆ 92 r Xˆ 2 Xˆ 91 Xˆ 1 Fig. 13. 43). The generalised force associated with the k-th generalised coordinate is given by (Leyko, 1996): Qk (P) = PT ∂r ∂qk for k = 1, . . 80a) where P is the force expressed in the global system { } and r is the vector of coordinates of the point at which force P acts in the system { }.

1984, 1999) the assumption that the components of the vector of generalised coordinates ˜ (p,i) are small always applies.

1 Division of the Flexible Link 37 Fig. 3. Division of a machine tool into rfes and sdes formulae and equations of motion of a flexible link discretised by means of the rfe method, as well as those of the whole kinematic chain to which the flexible link is appended. 1 Division of the Flexible Link into Rigid Finite Elements and Spring–Damping Elements Let us first consider the simple case when link p is a prismatic beam. 5 presents the model considered. First, the beam of length L(p) is divided into m(p) sections of equal length ∆(p) .

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